mathematics

SMP (computer algebra system)

SMP (computer algebra system) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand SMP (computer algebra system) rather than just read about it. In short: Symbolic Manipulation Program (SMP) was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979.

Key takeaways

SMP (computer algebra system) belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect SMP (computer algebra system) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of SMP (computer algebra system) from memory before moving on to harder problems.

Reference excerpt

Symbolic Manipulation Program (SMP) was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979. It was initially developed in the Caltech physics department with contributions from Geoffrey C. Fox, Jeffrey M. Greif, Eric D. Mjolsness, Larry J. Romans, Timothy Shaw, and Anthony E. Terrano.

History SMP was first sold commercially in 1981, by the Computer Mathematics Corporation of Los Angeles, which later became part of Inference Corporation. Inference further developed the program and marketed it commercially from 1983 to 1988, but it was not a commercial success, and Inference became pessimistic about the market for symbolic math programs, and so abandoned SMP to concentrate on expert systems. SMP was influenced by the earlier computer algebra systems Macsyma (of which Wolfram was a user) and Schoonschip (whose code Wolfram studied). SMP follows a rule-based approach, giving it a "consistent, pattern-directed language". Unlike Macsyma and Reduce, it was written in C. During the 1980s, it was one of the generally available general-purpose computer algebra systems, along with Reduce, Macsyma, and Scratchpad, and later muMATH and Maple. It was often used for teaching college calculus. The design of SMP's interactive language and its "map" commands influenced the design of the 1984 version of Scratchpad.

Reception SMP has been criticized for various characteristics, notably its use of floating-point numbers instead of exact rational numbers, which can lead to incorrect results, and makes polynomial greatest common divisor calculations problematic. Many other problems in early versions of the system were purportedly fixed in later versions.

References

Additional sources Chris A. Cole, Stephen Wolfram, "SMP: A Symbolic Manipulation Program", Proceedings of the fourth ACM symposium on Symbolic and algebraic computation (SIGSAM), Snowbird, Utah, 1981. full text Stephen Wolfram with Chris A. Cole, SMP: A Symbolic Manipulation Program, Reference Manual, California Institute of Technology, 1981; Inference Corporation, 1983. full text Stephen Wolfram, "Symbolic Mathematical Computation", Communications of the ACM, April 1985 (Volume 28, Issue 4). Despite the general-sounding title the focus is on an introduction to SMP. Online version of this article J.M. Greif, "The SMP Pattern-Matcher" in B.F. Caviness (editor), Proceedings of EUROCAL 1985, volume 2, pgs. 303-314, Springer-Verlag Lecture Notes in Computer Science, no. 204, ISBN 3-540-15984-3 A discussion, with examples, of the capabilities, tasks, and design philosophy of the pattern-matcher. SMP's manual "SMP Handbook" Stephen Wolfram's blog post on the history of SMP's creation

Worked examples

Example 1 — a first encounter with SMP (computer algebra system)

Start with the simplest possible case. Write down what SMP (computer algebra system) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to SMP (computer algebra system) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about SMP (computer algebra system) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of SMP (computer algebra system)

In research: SMP (computer algebra system) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses SMP (computer algebra system) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: SMP (computer algebra system) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computer algebra systems, so understanding it makes those chapters shorter.
In everyday life: Look for SMP (computer algebra system) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study SMP (computer algebra system) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what SMP (computer algebra system) means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain SMP (computer algebra system) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is SMP (computer algebra system) in simple terms?

Symbolic Manipulation Program (SMP) was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979.

Why does SMP (computer algebra system) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study SMP (computer algebra system)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on SMP (computer algebra system).